# Expanding Double Brackets Rules

When multiplying double parentheses, each term in the first pair of parentheses must be multiplied by each term in the second. a) Do not forget to multiply each term inside the brackets by the term outside: Multiply two brackets (x + 2)(x + 3) (2x – 7)(x – 4) (3x – 7)(4y – 1) (4x – 7)(4x + 7) (3x – 2)2 Multiply the first elements in square brackets: (y times y = y^2) In the second method, we divide each bracket into a grid, and then simply multiply each bit together. For both methods, we then simplify the intermediate terms of 3x – 5x = -2x, so that the final answer is x2 – 2x – 15. For triple parentheses: First expand the first two parentheses, then multiply this answer by the third parenthesis. Expanding parentheses removes parentheses from an expression by multiplying parentheses. This is achieved by multiplying each term inside the parenthesis by the term outside the parenthesis. Examples, solutions, and videos to help GCSE mathematics students learn how to extend algebraic expressions by extending double parentheses (pairs). Another method of multiplying parentheses is to use a grid. Be very careful when multiplying parentheses with many negative signs: begin{aligned} 7(3n – 9) – 4(6 – 4n) & = 21n – 63 – 24 + 16n & = 37n – 87end{aligned} Develop double brackets How to elaborate (extend) double brackets in algebra. (x – 3) (x + 4) (2x + 5) (x – 4) (k to 3) (k + 4) (p – q) (2p – 3q) (5 – t)2 (y – 4)(y + 4) If you write two parentheses next to each other, the parentheses must be multiplied together. For example, ((y + 2)(y + 3)) means ((y + 2) times (y + 3)).

When you expand double parentheses, each term in the first parenthesis must be multiplied by each term in the second parenthesis. It is useful to always multiply the terms in order so that none is forgotten. A common method is FOIL: First, Outside, Inside, Last. Here is an example of an extension with variables a, b, and c instead of numbers: The following diagram shows how to extend the pairs using the FOIL and Grid methods. Scroll down for more examples and solutions. Quadratic – Expansion of double brackets An introduction to the expansion of parentheses as required for Module 8 Unit 8 of the OCR Mathematics GCSE course. Some sample questions for you to try examples and solutions. (x + 2) (x + 3) (x + 2) (x – 4) (x – 3) (x – 6) (x + 2) (x + 5) (x + 7) (x – 2) (x – 4) (x – 5) When we develop double brackets, we must remember that in algebra means that two things are side by side, which means that they are multiplied. (x – 5) (x + 3) is the same as (x – 5) × (x + 3). We must therefore multiply everything in the second tranche by everything in the first tranche.

When developing parentheses, be very careful when dealing with negative numbers. In this case, −3 · -5 = +15 (a positive answer), but here is an example where the second part is negative: the letters can be used to represent unknown values or values that can change. Formulas can be written and equations solved to find solutions to a range of scientific and technological problems. (2m) and (-3m) are similar terms because they both contain the letter (m). And heres a hint: if a multiplication is obvious (like a ·2), do it right away, but if it requires more thought (like a·−b), leave it for the next line. What is in the ( ) should be treated as a „package”. In algebra, juxtaposing two things usually means multiplying. So((2m – 3)(m + 1) = 2m ^ 2 – 3m + 2m – 3 = 2m ^ 2 – m – 3 ). Simplify terms similar to ((3y + 2y)) to (y^2 + 5y + 6). So the second term ended negatively, because 2x · −a = −2ax (it is also more pleasant to write „−2ax” instead of „−2xa”). There are 2 different methods.

In the first method, we draw arcs that connect each term of the first hook to each term of the 2nd hook. x multiplied by x is x squared, x multiplied by 3 is 3x, -5 multiplied by x is -5x and -5 multiplied by 3 is -15. At the end we have 4 leaves; This is really important – to make sure we havent accidentally missed any. Some people like to remember FOIL: First, Outer, Inner, Last. It was also interesting because x was squared (x2). And here`s another example with some numbers. Note that the „·” between 3 and 6 means multiplication, so 3·6 = 18: c) If you multiply more complicated terms, multiply the numbers first, followed by the letters: Related Topics: Additional Lessons for GCSE Maths Math Spreadsheets. So, when multiplying: multiply by everything in the „package”. First, multiply each bracket, then collect the same terms: begin{aligned} 2(3x + 4) + 4(x – 1) & = 6x + 8 + 4x – 4 & = 10x + 4 end{aligned} Remember, if you multiply two negative terms, you get a positive: begin{aligned} (3x – 10)(5x – 9) & = 15x^2 – 27x – 50x + 90 & = 15x^2 – 77x + 90\end{aligned} „Expand” means delete the ( ). But we have to get it right! If you multiply (x) by another (x), you get a term (x^2): begin{aligned} (x + 4)(x + 3) & = x^2 + 3x + 4x + 12 & = x^2 + 7x + 12 end{aligned}. Finally, we have an example with three terms:.